[Thork]

No. I was never given a real world example of any gradient calculation with a curved earth. Still waiting. Will continue to wait.

And we have 3 North's. Magnetic North, Grid North and True North. However the only one of those you don't use to navigate is the round earth abomination True North.

[Rama Set]

No. I was never given a real world example of any gradient calculation with a curved earth. Still waiting. Will continue to wait.

Not for long!

I did find a graph of nile elevation vs distance, so feel free to calculate the gradient at any point as was discussed above:



Note that in geography, elevation is defined as:

elevation - (1)The distance of a point above a specified surface of constant potential; the distance is measured along the direction of gravity between the point and the surface.
The surface usually specified is the geoid or an approximation thereto. Mean sea level was long considered a satisfactory approximation to the geoid and therefore suitable for use as a reference surface. It is now known that mean sea level can differ from the geoid by up to a meter but the exact difference is difficult to determine. The terms height and level are frequently used as synonyms for elevation. In geodesy, height also refers to the distance above an ellipsoid; it is used in this sense in this glossary, except where custom has established a different usage. "Level" has such a variety of meanings that it is best not to use the term to mean elevation.

It is evident that you can derive the gradient at any point from this graph.

And we have 3 North's. Magnetic North, Grid North and True North. However the only one of those you don't use to navigate is the round earth abomination True North.

Red Herring.

[markjo]

No. I was never given a real world example of any gradient calculation with a curved earth. Still waiting. Will continue to wait.

And we have 3 North's. Magnetic North, Grid North and True North. However the only one of those you don't use to navigate is the round earth abomination True North.

Incorrect.

The grid lines on Ordnance Survey maps divide the UK into one-kilometre squares, east of an imaginary zero point in the Atlantic Ocean, west of Cornwall. The grid lines point to a Grid North, varying slightly from True North. This variation is smallest along the central meridian (north-south line) of the map, and greatest at the map edges. The difference between grid north and true north is very small and can be ignored for most navigation purposes. The difference exists because the correspondence between a flat map and the round Earth is necessarily imperfect.